Giovanna Devetag

Games and phone numbers: do short term memory bounds affect strategic behavior?

Research in experimental and behavioral game theory has revealed a substantial and persistent degree of heterogeneity in the strategic behavior of real individuals. While the prevailing theoretical explanations of the observed heterogeneity typically invoke underlying differences in beliefs among the population of players, we argue that a further source of heterogeneity may consist in the individuals different ability to process information, of which short term memory capacity provides a measurable proxy. Research in cognitive psychology has shown that individuals typically differ in their short term memory capacity; furthermore, short term memory capacity provides a fundamental cognitive bottleneck to our ability to process information efficiently and hence seems correlated with performance in a variety of problem solving and reasoning tasks. In this paper we conduct experiments on a set of well-known games whose solution concepts require the application of some paradigmatic forms of strategic reasoning, such as iterated dominance, reasoning about common knowledge and backward induction. We separately conduct standard short term memory tests on our subjects to detect the presence of a correlation between individuals behavior in the games - here defined in terms of degrees of conformity to the standard game-theoretic prescriptions - and their short term memory score. Our results show the presence of a significant and positive correlation between subjects short term memory score and conformity to standard game-theoretic prescriptions in the games, thus confirming our hypothesis. While the robustness of our conjecture awaits to be confirmed by further data gathering in more interactive experimental settings, our preliminary results suggest a promising line of inquiry on the interconnections between information processing capacity and strategic behavior

Playing the Wrong Game: An Experimental Analysis of Relational Complexity and Strategic Misrepresentation

It has been suggested that players often produce simplified and/or misspecified mental models of strategic decisions [Kreps, D., 1990. Game Theory and Economic Modeling. Oxford Univ. Press, Oxford]. We submit that the relational structure of players preferences in a game is a source of cognitive complexity, and may be an important driver of such simplifications. We provide a classification of order structures in two-person games based on the properties of monotonicity and projectivity, and present experiments in which subjects construct representations of games of different relational complexity and subsequently play the games according to these representations. Experimental results suggest that relational complexity matters. More complex games are harder to represent, and this difficulty seems correlated with short term memory capacity. In addition, most erroneous representations are simpler than the correct ones. Finally, subjects who misrepresent the games behave consistently with such representations, suggesting that in many strategic settings individuals may act optimally on the ground of simplified and mistaken premises.

Coordination and Information in Critical Mass Games: An Experimental Study

We present experimental results on a repeated coordination game with Pareto-ranked equilibria in which a payoff from choosing an action is positive only if a critical mass of players choose that action. We design a baseline version of the game in which payoffs remain constant for values above the critical mass, and an increasing returns version in which payoffs keep increasing for values above the critical mass. We test the predictive power of security and payoff-dominance under different information treatments. Our results show that convergence to the payoff-dominant equilibrium is the modal limit outcome when players have full information about others previous round choices, while this outcome never occurs in the remaining treatments. The paths of play in some groups reveal a tacit dynamic coordination by which groups converge to the efficient equilibrium in a step-like manner. Moreover, the frequency and speed of convergence to the payoff-dominant equilibrium are higher, ceteris paribus, when increasing returns are present. Finally, successful coordination seems to crucially depend on players willingness to signal to others the choice of the action supporting the efficient equilibrium.

A laboratory experiment on the minority game

This work presents experimental results on a coordination game in which agents must repeatedly choose between two sides, and a positive fixed payoff is assigned only to agents who pick the minoritarian side. We conduct laboratory experiments in which stationary groups of five players play the game for 100 periods, and manipulate two treatment variables: the amount of ‘memory’ M that players have regarding the game history (i.e., the length of the string of past outcomes that players can see on the screen while choosing) and the amount of information about other players’ past choices. Our results show that, at the aggregate level, a quite remarkable degree of coordination is achieved. Moreover, providing players with full information about other players’ choice distribution does not appear to improve efficiency significantly.

Coordination and Self-Organization in Minority Games: Experimental Evidence

This work presents experimental results on a coordination game in which agents must repeatedly choose between two sides, and a positive fixed payoff is assigned only to agents who pick the minoritarian side. The game presents a variety of asymmetric pure strategy equilibria, and a unique symmetric mixed-strategy equilibrium in which agents randomize between the two sides at every stage. The game reflects some essential features of those economic situations in which positive rewards are assigned to individuals who behave in opposition to the modal behavior in a population. We conduct laboratory experiments in which stationary groups of five players play the game for 100 periods, and manipulate two treatment variables: the amount of memory M that players have regarding the game history (i.e., the length of the string of past outcomes that players can see on the screen while choosing), and the amount of information about other players past choices: in the aggregate information treatment, players only know which side was the minority side at each period, while in the full information treatment players have information regarding the entire distribution of choices in the group at each round. We first analyze aggregate results in terms of both allocative and informational efficiency. We then analyze individual behavior in the game as compared to the theoretical benchmark provided by the mixed strategy equilibrium solution. Our results show that, first, both allocative and informational efficiency are higher on average than the benchmark value corresponding to the mixed strategy equilibrium in all treatments, suggesting that a quite remarkable degree of coordination is achieved; second, providing players with full information about other players choice distribution does not appear to improve efficiency significantly. At the individual level, a substantial portion of subjects exhibit `inertial behavior, i.e., the tendency to replicate their previous round choice with a higher frequency than the one prescribed by randomizing behavior, and such inertia seems to be enhanced rather than decreased by a full information treatment.

Expectations Structure in Asset Pricing Experiments

Notwithstanding the recognized importance of tradersi?½ expectations in characterizing the observed market dynamics, for instance the formation of speculative bubbles and crashes on financial markets, little attention has been devoted so far by economists to a rigorous study of expectation formation in the laboratory. In this work we describe a laboratory experiment on the emergence and coordination of expectations in a pure exchange framework. We largely base our study on previous experiments on expectation formation in a controlled laboratory environment by Cars Hommes, Joep Sonnemans, Ian Tuinstra and Henk van de Velden (2002a). We consider a simple two asset economy with a riskless bond and a risky stock. Each market is composed of six experimental subjects who act as financial advisors of myopic risk-averse utility maximizing investors and are rewarded according to how well their forecasts perform in the market. The participants are asked to predict not only the price of the risky asset at time t+1, as in Hommes et al. (2002a), but also the confidence interval of their prediction, knowing the past realizations of the price until time t i?½ 1. The realized asset price is derived from a Walrasian market equilibrium equation, unknown to the subjects, with feedback from individual forecasts. Subjectsi?½ earnings are proportional to the increase in their wealth level. With respect to previous experiments that did not include an explicit evaluation of risk by participants, we observe a higher price volatility, a decreased likelihood of bubble dynamics and, in general, a higher heterogeneity of predictions.

Classic coordination failures revisited: the effects of deviation costs and loss avoidance

Are communication failures common? We revisit a classic example of experimental coordination failure and explore, in a 2x2 design, the effects of deviation costs and loss avoidance. Our results suggest how to engineer coordination successes in the laboratory, and possibly in the wild.

Representing others' preferences in mixed motive games: was Schelling right

The available experimental evidence suggests that even two-person normal form games with an elementary action space present substantial degrees of cognitive difficulty. We submit that the relational structure of the players preferences is a source of complexity of a game. We provide a formal classification of order structures in two-person normal form games based on the two properties of monotonicity and projectivity, and present an experiment on individual ability to construct a representation of bi-ordered sets isomorphic to the preference structure of paradigmatic normal form games. Experimental results support the hypothesis that relational complexity matters. In particular, they support Schellings intuition that mixed motive games are harder to represent than pure motive ones. In addition, the experiment shows that most subjects tend to perceive and extract monotonic relations from non-projective ones. We show that individuals short term memory capacity limitations significantly affect their ability to correctly represent bi-orders.

Exploring the Effects of Real Effort in a Weak-Link Experiment

We report results from a weak-link i?½ often also called minimum-effort i?½ game experiment with multiple Pareto-ranked strict pure-strategy Nash equilibria, using a real-effort rather than a chosen-effort task: subjects have to sort and count coins and their payoff depends on the worst performance in the group. While in the initial rounds our subjects typically coordinate on inefficient outcomes, almost 80 percent of the groups are able to overcome coordination failure in the later rounds. Our results are in stark contrast to results typically reported in the literature.

Solving Coordination Problems Experimentally

We discuss four major classes of coordination problems: pure coordination or rendezvous games; Pareto-ranked coordination games such as stag-hunt and order-statistic games; mixed-motives coordination games such as “Battle-of-the-Sexes”; and critical-mass games. We review “classic” implementations of exemplars of the four classes of coordination problems. En passant, we discuss experimental practices in economics. We conclude with an assessment of the literature: we discuss what we have learned so far from the literature as well as what we consider particularly promising avenues of future research.